Effect Of Streamwise Pressure Gradient Research Articles

Global Stability Analysis of Spatially Developing Boundary Layer: Effect of Streamwise Pressure Gradients

The paper presents a global stability analysis of the two-dimensional incompressible boundary layer with the effect of streamwise pressure gradient. A symmetric wedge flow is considered at different values of the dimensionless pressure gradient parameter βH. The pressure gradient dp/dx in the flow direction is zero, when βH = 0, favorable (negative) for βH > 0, and adverse (positive) for βH < 0. The base flow is computed by numerical solution of Falkner—Skan equation. The Reynolds number is based on the displacement thickness δ* at the inflow boundary. The stability equations governing the flow are derived in body-fitted coordinates. The stability equations are discretized using the Chebyshev spectral collocation method. The discretized equations, together with boundary conditions, form a general eigenvalue problem and are solved using Arnoldi’s algorithm. The temporal global modes are computed for βH = 0.022, 0.044, and 0.066, for favorable and adverse pressure gradients. The temporal growth rate ωi is found to be negative for all the global modes. The ωi value is smaller for the favorable pressure gradient (FPG) than for the adverse pressure gradient (APG) at the same Reynolds number (Re = 340). Thus, the FPG has a stabilizing effect on the boundary layer. The comparison of the spatial eigenmodes and spatial amplification rates for FPG and APG show that FPG has a stabilizing effect, whereas APG has a destabilizing effect on the disturbances.

RANS simulation of high-Re turbulent flows using an immersed boundary method in conjunction with wall modeling

Abstract In this paper, an immersed boundary method, called the domain-free discretization (DFD) method, is developed to simulate the turbulent flows at high Reynolds numbers governed by the RANS equations. The strategy of DFD is that the discrete form of partial differential equations at an interior mesh node may involve some nodes outside the solution domain. Wall-modeling techniques, such as the adaptive wall function and the two-layer wall model, are adopted to alleviate the requirement on the near-wall mesh size. In the two-layer wall model, the effect of streamwise pressure gradient can be taken into account. The no-penetration condition and the wall shear stress prescribed by wall modeling, instead of the no-slip condition, are enforced at the immersed boundary. The normal and tangential velocity components at an exterior dependent node are evaluated via the linear extrapolation in the normal direction in conjunction with the no-penetration condition and the prescribed shear stress, respectively. The pressure at an exterior dependent node is obtained by solving the simplified momentum equation, and the temperature is calculated via the Crocoo-Busemann relation. By using analytical solutions, appropriate boundary conditions for the SST k − ω turbulence model equations are specified and then the turbulence variables at an exterior dependent node are determined. Various subsonic and transonic high-Re turbulent flows over stationary and moving bodies have been simulated to validate the present developed DFD method.

Effects of wall curvature and streamwise pressure gradient on film cooling effectiveness

As the load of a modern turbine is increasing, the turning angle and the flow acceleration is increasing. The effects of streamwise pressure gradient (SPG) and wall curvature on film cooling performance are becoming more and more important. Film cooling effectiveness with those two effects was investigated experimentally and numerically. Flow on the concave wall has an unstable effect and increases the turbulence intensity which leads to a faster dissipation and wider lateral spreading. With these two opposite effects, there is a critical point that when the momentum ratio is smaller than the certain value, film cooling effectiveness is highest on concave wall and the rank is opposite when the momentum ratio is larger than the value. The critical momentum ratio is 0.6 with nonaccelerated main flow for all density ratios. For the cases with different SPG, the critical momentum ratio still exists, while the value increases with stronger favorable pressure gradient and ranges from 0.55 to 0.75 in the present research. The film cooling performance with different SPG and wall curvature is quite different from the flat wall case and thus these effects should be taken into consideration in gas turbine film cooling design.

A deterministic model for the sublayer streaks in turbulent boundary layers for application to flow control

We present a relatively simple, deterministic, theoretical model for the sublayer streaks in a turbulent boundary layer based on an analogy with Klebanoff modes. Our approach is to generate the streamwise vortices found in the buffer layer by means of a vorticity source in the form of a fictitious body force. It is found that the strongest streaks correspond to a spanwise wavelength that lies within the range of the experimentally observed values for the statistical mean streak spacing. We also present results showing the effect of streamwise pressure gradient, Reynolds number and wall compliance on the sublayer streaks. The theoretical predictions for the effects of wall compliance on the streak characteristics agree well with experimental data. Our proposed theoretical model for the quasi-periodic bursting cycle is also described, which places the streak modelling in context. The proposed bursting process is as follows: (i) streamwise vortices generate sublayer streaks and other vortical elements generate propagating plane waves, (ii) when the streaks reach a sufficient amplitude, they interact nonlinearly with the plane waves to produce oblique waves that exhibit transient growth, and (iii) the oblique waves interact nonlinearly with the plane wave to generate streamwise vortices; these in turn generate the sublayer streaks and so the cycle is renewed.

Impingement Heat Transfer, Part II: Effect of Streamwise Pressure Gradient

This is Part II of a two-part paper on jet-impingement heat transfer. The effect of streamwise pressure gradient on jet-impingement heat transfer is investigated. In realistic configurations, impingement arrays do not always impinge in channels that have parallel walls. Converging channels create positive pressure gradient, and diverging channels create adverse pressure gradient. In this study, the effect of nonparallel walls on jet-impingement heat transfer is investigated. Firstly for impingement arrays with jet-to-jet streamwise and spanwise spacing of fourhole diameters and eight-hole diameters and then for the linearly stretched arrays discussed in Part I. Two jet Reynolds numbers are studied for all cases for Re =6 × × 10 3 , and 10 3 . Also, the jet height-to-diameter ratio is increased from 1 to 5 to generate the adverse pressure gradient and decreased from 5 to 1 to generate the positive pressure gradient. Results show that the effect of streamwise pressure gradient alters the flow distribution causing significant variations in heat-transfer distributions. Accelerating flow causes streamwise jet stretching, whereas decelerating flow causes spanwise jet stretching. The results for converging and diverging channels are compared with results for parallel plate channels with different spacing to compare the effect of the streamwise pressure gradient.

Simulation of boundary layer transition induced by periodically passing wakes

The interaction between an initially laminar boundary layer developing spatially on a flat plate and wakes traversing the inlet periodically has been simulated numerically. The three-dimensional, time-dependent Navier–Stokes equations were solved with 5.24×107 grid points using a message passing interface on a scalable parallel computer. The flow bears a close resemblance to the transitional boundary layer on turbomachinery blades and was designed following, in outline, the experiments by Liu &amp; Rodi (1991). The momentum thickness Reynolds number evolves from Reθ = 80 to 1120. Mean and second-order statistics downstream of Reθ = 800 are of canonical flat-plate turbulent boundary layers and are in good agreement with Spalart (1988).In many important aspects the mechanism leading to the inception of turbulence is in agreement with previous fundamental studies on boundary layer bypass transition, as summarized in Alfredsson &amp; Matsubara (1996). Inlet wake disturbances inside the boundary layer evolve rapidly into longitudinal puffs during an initial receptivity phase. In the absence of strong forcing from free-stream vortices, these structures exhibit streamwise elongation with gradual decay in amplitude. Selective intensification of the puffs occurs when certain types of turbulent eddies from the free-stream wake interact with the boundary layer flow through a localized instability. Breakdown of the puffs into young turbulent spots is preceded by a wavy motion in the velocity field in the outer part of the boundary layer.Properties and streamwise evolution of the turbulent spots following breakdown, as well as the process of completion of transition to turbulence, are in agreement with previous engineering turbomachinery flow studies. The overall geometrical characteristics of the matured turbulent spot are in good agreement with those observed in the experiments of Zhong et al. (1998). When breakdown occurs in the outer layer, where local convection speed is large, as in the present case, the spots broaden downstream, having the vague appearance of an arrowhead pointing upstream.The flow has also been studied statistically. Phase-averaged velocity fields and skin-friction coefficients in the transitional region show similar features to previous cascade experiments. Selected results from additional thought experiments and simulations are also presented to illustrate the effects of streamwise pressure gradient and free-stream turbulence.

Modification of near-wall turbulence structure in a shear-driven three-dimensional turbulent boundary layer

Most high Reynolds number flows of engineering interest are three-dimensional in nature. Key features of three-dimensional turbulent boundary layers (3DTBLs) include: non-colateral shear stress and strain rate vectors, and decreasing ratio of the shear stresses to the turbulent kinetic energy with increasing three-dimensionality. These are indicators that the skewing has a significant effect on the structure of turbulence. In order to further investigate the flow physics and turbulence structure of these complex flows, an innovative method for generating a planar shear-driven 3DTBL was developed. A specialized facility incorporating a relatively simple geometry and allowing for varying strengths of crossflow was constructed to facilitate studies where the skewing is decoupled from the confounding effects of streamwise pressure gradient and curvature. On-line planar particle image velocimetry (PIV) measurements and flow visualization results indicate that the experimental configuration generates the desired complex flow, which exhibits typical characteristics associated with 3DTBLs. Furthermore, spanwise shear results in modification of the near-wall turbulence structure. Analysis of near-wall flow visualization photographs revealed a reduction of mean streak length with increasing spanwise shear, while streak spacing remained relatively constant. In the most strongly sheared case, where the belt velocity is twice that of the freestream velocity, the mean streak length was reduced by approximately 50%.

Effect of streamwise pressure gradient on the supersonic mixing layer

Effect of streamwise pressure gradient on the supersonic mixing layer

Influence of the Side Walls on the Turbulent Center-Plane Boundary-Layer in a Square Duct

Measurements in the entry region of a square duct (specifically, a wind-tunnel working section) show that the direct effect of stress-induced secondary flows in the corners on the center-plane boundary layer is negligible for boundary layers thinner than about one-fourth of the duct width. Further, the effects of streamwise pressure gradient and of quasi-collinear lateral convergence tend to cancel so that the velocity profiles and skin friction are quite close to those on a flat plate. This shows that the boundary layer on the floor of a wind tunnel of constant, square cross section can be used to simulate a flat-plate flow even when the boundary layer thickness is as large as one-fourth of the tunnel height.

Combustion in the Laminar Boundary Layer of Chemically Active Sublimating Surfaces

A DETAILED ANALYSIS has been carried out in reference 1 for the heat and mass transfer from sublimating surfaces where the sublimated material subsequent^ reacts with the atmosphere. The boundary-layer equations were transformed in the conventional manner and the effects of streamwise pressure gradients neglected in accordance with the argument of Lees, reference 2. If the diffusion coefficients of all species present are equal, if Pr = Le = 1, and if pfj, = constant, then the heat and mass transfer can be estimated with very little detailed knowledge of the chemical reactions in the boundary laj^er. Under these conditions the mass fractions Tm of atomic species m, irrespective of molecular configuration, and the total enthalpy hs, including the chemical enthalpy, can be expressed as linear functions of the velocity ratio u/ue where ue is the velocity at the outer edge of the boundary layer. Fast combustion reactions of the type